Nonlinear Energy Sink With Uncertain Parameters

[+] Author and Article Information
E. Gourdon, C. H. Lamarque

ENTPE, LGM, URA CNRS 1652, Rue Maurice Audin, 69518 Vaulx en Velin Cedex, France

J. Comput. Nonlinear Dynam 1(3), 187-195 (Mar 02, 2006) (9 pages) doi:10.1115/1.2198213 History: Received May 19, 2005; Revised March 02, 2006

The effects of a nonlinear energy sink during the instationary regime are analyzed by introducing uncertain parameters to verify the robustness of the transient spatial energy transfer when parameters are not well known. It was shown that it is possible to passively absorb energy from a linear nonconservative system (damped) structure to a nonlinear attachment weakly coupled to the linear one. This rapid and irreversible transfer of energy, named energy pumping, is studied by taking into account uncertainties on parameters, especially damping (since damping plays a great role and there is a lack of knowledge about it). In essence, the nonlinear subsystem acts as a passive nonlinear energy sink for impulsively applied external vibrational disturbances. The aim is to be able to apply energy pumping in practice where the nonlinear attachment realization will never perfectly reflect the design. Since strong nonlinearities are involved, polynomial chaos expansions are used to obtain information about random displacements. Not only are numerical investigations done, but nonlinear normal modes and the role of damping are also analytically studied, which confirms the numerical studies and shows the supplementary information obtained compared to a parametrical study.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

General system with 2 DOF

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Figure 2

Means and standard deviations of oscillators without and with coupling using a chaos of order 2 and with C uncertain

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Figure 3

Polynomial chaos expansion of order 2 (solid line): comparison to a Monte Carlo simulation (dotted line)

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Figure 4

Means and standard deviations of oscillators without and with coupling and energy ratio (mean and standard deviation) in the nonlinear oscillator using a chaos of order 2 and with c1 uncertain

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Figure 5

Global analytical calculation of nonlinear normal modes: stable inverse mode localization conversion with F0=20, F1=0.1F0, or F1=0.3F0

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Figure 6

Curves with two saddle-node bifurcations in some cases (a10=1.5 or a10=4.5 and a11=40%×a10)

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Figure 7

Occurrence or not of the bifurcation (a10=2.4 and a11=0 or a11=40%×a10)




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